The goal of this project is to improve magnetic resonance temperature imaging (MRTI) techniques to be used in high intensity focused ultrasound (HIFU) thermal treatments by significantly expanding their current spatial and temporal resolution and field of view (FOV) capabilities. These improvements will overcome the speed, resolution, and FOV roadblocks in transcranial MRI guided focused ultrasound therapy and thereby accelerate the acceptance of this technique into clinical practice. To realize this goal we propose to develop a completely new MRTI approach that increases speed by subsampling the measurement space (k-space) in each time frame and that uses a subject-specific biophysical model incorporating inhomogeneous tissue biothermal and acoustic properties to dynamically (in real-time) predict the missing measurements. The uniqueness of this approach is that it supplements 3D MRTI with additional subject-specific biophysical information. We refer to this method as model predictive filtering (MPF) because it is similar to other linear predictive filters, such as the Kalman filter. This new MPF technique will achieve the required accurate, precise, and rapid high-resolution measurements of temperature distributions over regions sufficiently large to effectively monitor and control treatments in real-time. The work will develop methods to improve temperature measurements in three stages: 1) First a temporally-constrained reconstruction (TCR) technique will be developed to obtain retrospective MRTI measurements with high spatial and temporal resolution over the volume of interest. 2) The TCR temperatures combined with tissue segmentation and beam modeling will be used to determine 3D subject- specific tissue acoustic and thermal properties. 3) The tissue acoustic and thermal properties will be incorporated into the MPF technique to obtain the desired temperature images over the full insonified volume in real-time. These methods will then be tested in vivo in animal models and in vitro and ex vivo in a transcranial MRgHIFU system. Transcranial brain MRgHIFU is an important application that requires the development of innovative treatment strategies and will definitely require rapid, accurate, high spatial resolution temperature measurements over the entire insonified volume. These techniques are highly novel, and upon success will facilitate experiments to accelerate the acceptance of transcranial brain MRgHIFU as well as potentially other new MRgHIFU applications.